3.2 \(\int e^x \, dx\)

Optimal. Leaf size=3 \[ e^x \]

[Out]

E^x

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Rubi [A]  time = 0.0009641, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2194} \[ e^x \]

Antiderivative was successfully verified.

[In]

Int[E^x,x]

[Out]

E^x

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin{align*} \int e^x \, dx &=e^x\\ \end{align*}

Mathematica [A]  time = 0.0000985, size = 3, normalized size = 1. \[ e^x \]

Antiderivative was successfully verified.

[In]

Integrate[E^x,x]

[Out]

E^x

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Maple [A]  time = 0., size = 3, normalized size = 1. \begin{align*}{{\rm e}^{x}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x),x)

[Out]

exp(x)

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Maxima [A]  time = 0.91739, size = 3, normalized size = 1. \begin{align*} e^{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="maxima")

[Out]

e^x

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Fricas [A]  time = 1.79761, size = 7, normalized size = 2.33 \begin{align*} e^{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="fricas")

[Out]

e^x

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Sympy [A]  time = 0.039106, size = 2, normalized size = 0.67 \begin{align*} e^{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x)

[Out]

exp(x)

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Giac [A]  time = 1.05884, size = 3, normalized size = 1. \begin{align*} e^{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="giac")

[Out]

e^x